Adversarial risk analysis for counterterrorism modeling

Recent large-scale terrorist attacks have raised interest in models for resource allocation against terrorist threats. The unifying theme in this area is the need to develop methods for the analysis of allocation decisions when risks stem from the intentional actions of intelligent adversaries. Most approaches to these problems have a game-theoretic flavor although there are also several interesting decision-analytic-based proposals. One of them is the recently introduced framework for adversarial risk analysis, which deals with decision-making problems that involve intelligent opponents and uncertain outcomes. We explore how adversarial risk analysis addresses some standard counterterrorism models: simultaneous defend-attack models, sequential defend-attack-defend models, and sequential defend-attack models with private information. For each model, we first assess critically what would be a typical game-theoretic approach and then provide the corresponding solution proposed by the adversarial risk analysis framework, emphasizing how to coherently assess a predictive probability model of the adversary's actions, in a context in which we aim at supporting decisions of a defender versus an attacker. This illustrates the application of adversarial risk analysis to basic counterterrorism models that may be used as basic building blocks for more complex risk analysis of counterterrorism problems.     

Guiding Resource Allocations Based on Terrorism Risk

Establishing tolerable levels of risk is one of the most contentious and important risk management decisions. With every regulatory or funding decision for a risk management program, society decides whether or not risk is tolerable. The Urban Area Security Initiative (UASI) is a Department of Homeland Security (DHS) grant program designed to enhance security and overall preparedness to prevent, respond to, and recover from acts of terrorism by providing financial assistance for planning, equipment, training, and exercise needs of large urban areas. After briefly reviewing definitions of terrorism risk and rationales for risk-based resource allocation, this article compares estimates of terrorism risk in urban areas that received UASI funding in 2004 to other federal risk management decisions. This comparison suggests that UASI allocations are generally consistent with other federal risk management decisions. However, terrorism risk in several cities that received funding is below levels that are often tolerated in other risk management contexts. There are several reasons why the conclusions about terrorism risk being de minimis in specific cities should be challenged. Some of these surround the means used to estimate terrorism risk for this study. Others involve the comparison that is made to other risk management decisions. However, many of the observations reported are valid even if reported terrorism risk estimates are several orders of magnitude too low. Discussion of resource allocation should be extended to address risk tolerance and include explicit comparisons, like those presented here, to other risk management decisions.     

Resource allocation. The cost of care: two troublesome cases in health care ethics.

With the cost of health care rising rapidly, both physicians and administrators regularly face resource allocation decisions. Under these conditions of relative scarcity, the equitable and appropriate distribution of limited resources becomes an ethical as well as a financial issue. Through ethical analysis, physician executives can assist their physician colleagues and fellow administrators to find rationally defensible answers to questions regarding the distribution of limited resources. Six criteria are frequently "weighted in the balance" by ethicists when analyzing whether justice is served in the distribution of a limited resource: need, equality, contribution, ability to pay, effort, and merit. The authors argue that, from an ethical standpoint, the best single criterion upon which one can base an allocation decision is that of merit, defined as the potential to benefit from the investment of additional resources.     

A Risk-sharing Approach to Transfer Pricing and Incentive Compensation Problems under Exchange Rate Uncertainty*

This study examines the transfer pricing and incentive compensation problems in a multinational enterprise facing currency risk. It is shown that, in the presence of diverse risk preferences among managers, the Hirshleifer (1956) transfer pricing rule results in inefficient resource allocation decisions by division managers. Following the approach developed by Kanodia (1979), two transfer pricing and compensation systems are proposed. The proposed systems enable central management to achieve efficient resource allocation and partial or global risk sharing. It is also argued that the proposed plans can be implemented in conjunction with existing transfer pricing systems that primarily serve tax and tariff concerns.     

A solution framework for the multi-mode resource-constrained cross-dock scheduling problem

In this paper we propose a framework for shift-level container scheduling and resource allocation decisions at a cross-dock facility. The Multi-Mode Resource-Constrained Cross-Dock Scheduling Problem (MRCDSP) approach minimizes material flow and schedules inbound and outbound containers to dock-doors such that the total processing time is minimized subject to the resource constraints at the cross-dock. While container scheduling and resource allocation problems at cross-dock facilities have been studied previously in isolation, our work is the first to consider a complete view of cross-dock operations providing optimal container to dock-door allocation, and a makespan minimizing schedule of containers to the cross-dock. We present a comprehensive framework that includes identification of container clusters to reduce the problem size, a container-to-dock-door assignment algorithm, and a container clusters scheduling model that is solvable for practically sized problems. In a comparative numeric study based on data simulating a cross-dock facility, our approach is shown to outperform current practice, reducing the average time required for processing a set of containers by 37% and reducing the weighted-distance material traveled within the cross-dock by 45%.     

Modeling the Effectiveness of Respiratory Protective Devices in Reducing Influenza Outbreak

Outbreaks of influenza represent an important health concern worldwide. In many cases, vaccines are only partially successful in reducing the infection rate, and respiratory protective devices (RPDs) are used as a complementary countermeasure. In devising a protection strategy against influenza for a given population, estimates of the level of protection afforded by different RPDs is valuable. In this article, a risk assessment model previously developed in general form was used to estimate the effectiveness of different types of protective equipment in reducing the rate of infection in an influenza outbreak. It was found that a 50% compliance in donning the device resulted in a significant (at least 50% prevalence and 20% cumulative incidence) reduction in risk for fitted and unfitted N95 respirators, high‐filtration surgical masks, and both low‐filtration and high‐filtration pediatric masks. An 80% compliance rate essentially eliminated the influenza outbreak. The results of the present study, as well as the application of the model to related influenza scenarios, are potentially useful to public health officials in decisions involving resource allocation or education strategies.     

The Distribution of Risks: Vehicle Occupant Fatalities and Time of the Week

Automobile accident risks vary significantly across populations, places, and times. This study describes the time-varying pattern of societal risk. The relative risks of occupant fatality per person-mile of travel are estimated here for each hour of the week, using 1983 data. The results exhibit a strong time-of-day effect and have a highly skewed frequency distribution, implying wide variations in risk-taking behavior. Indeed, the 168 hourly estimates ranged from a low of 0.32 times the average around Sunday noon to a high of 43 times the average at 3:00 a.m. on Sunday, i.e., by a factor of 134 from bottom to top. Quantile-quantile plots or "Lorenz curves," introduced to display the unequal distribution of risks, show that approximately 34% of the vehicle occupant fatalities occur in hours representing only 5% of the travel. These findings have serious implications for risk analysis. First, when attempting to reconcile objective and subjective risk estimates, risk communicators should carefully control for when and to whom the risk in question is applicable. Second, comparisons of hazards on the basis of average risk are necessarily misleading for risks distributed so unevenly. Third, resource allocation decisions can benefit by knowing how incidence, exposure, and risk vary across time, place, and other relevant variables. Finally, certain cost-benefit analyses that use average values to estimate risk exposure can be misleading.     

Integrating Operational and Organizational Aspects in Interdependent Infrastructure Network Recovery

Managing risk in infrastructure systems implies dealing with interdependent physical networks and their relationships with the natural and societal contexts. Computational tools are often used to support operational decisions aimed at improving resilience, whereas economics‐related tools tend to be used to address broader societal and policy issues in infrastructure management. We propose an optimization‐based framework for infrastructure resilience analysis that incorporates organizational and socioeconomic aspects into operational problems, allowing to understand relationships between decisions at the policy level (e.g., regulation) and the technical level (e.g., optimal infrastructure restoration). We focus on three issues that arise when integrating such levels. First, optimal restoration strategies driven by financial and operational factors evolve differently compared to those driven by socioeconomic and humanitarian factors. Second, regulatory aspects have a significant impact on recovery dynamics (e.g., effective recovery is most challenging in societies with weak institutions and regulation, where individual interests may compromise societal well‐being). And third, the decision space (i.e., available actions) in postdisaster phases is strongly determined by predisaster decisions (e.g., resource allocation). The proposed optimization framework addresses these issues by using: (1) parametric analyses to test the influence of operational and socioeconomic factors on optimization outcomes, (2) regulatory constraints to model and assess the cost and benefit (for a variety of actors) of enforcing specific policy‐related conditions for the recovery process, and (3) sensitivity analyses to capture the effect of predisaster decisions on recovery. We illustrate our methodology with an example regarding the recovery of interdependent water, power, and gas networks in Shelby County, TN (USA), with exposure to natural hazards.     

基于随机理论的多项目资源配置模型及应用研究

为解决多项目管理中共享资源配置问题,在对信息环境下企业资源特点研究的基础上,应用随机理论确定了企业资源多项目并行配置时的资源等效效率和效率转换系数,由此建立了资源配置效率模型,通过对其数学方程的分析给出了相应的算法.运用该模型和算法,通过实例分析实现了资源的合理配置.     

The Fairness of Decision Rules

Prior work on resource allocation has generally considered only a small number of allocation rules, usually reflecting equity or equality. We use a scenario study to examine the effect of eight different allocation rules (past performance, future performance, rank, random draw, chance meetings, business need, personal need, and political reasons) on recipient reactions to the gain or loss of three different kinds of resources in an organizational setting. We find evidence that allocations based on past performance and random draw rules lead to the highest fairness perceptions and the lowest expectations that the decisions made will lead to intragroup conflict. However, fairness judgments are also influenced by a variety of other factors, such as the type of resource being allocated and whether the recipient is advantaged or disadvantaged relative to others in the workgroup (what we term the “egocentric interaction”). We discuss how our results might influence managers’ allocation decisions.     

An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations

This paper addresses the resource-constrained project scheduling problem with uncertain activity durations. An adaptive robust optimization model is proposed to derive the resource allocation decisions that minimize the worst-case makespan, under general polyhedral uncertainty sets. The properties of the model are analyzed, assuming that the activity durations are subject to interval uncertainty where the level of robustness is controlled by a protection factor related to the risk aversion of the decision maker. A general decomposition approach is proposed to solve the robust counterpart of the resource-constrained project scheduling problem, further tailored to address the uncertainty set with the protection factor. An extensive computational study is presented on benchmark instances adapted from the PSPLIB.     

内部资本市场跨期配置下最优分部相关性匹配研究——对多元化企业并购整合内在逻辑的诠释

内部资本市场跨期配置是研究多元化整合的新视角，分部相关性是平衡跨期配置成本和配置空间的关键因素。已有研究认为多元化企业存在最优分部相关性，但最优分部相关性的影响因素及其匹配规律尚未明确。借鉴实物期权的定价思路，基于动态规划方程的二叉树数值分析方法，研究了内部资本市场跨期配置下的最优分部相关性匹配问题。基于跨期配置的执行力和适应力，理论部分刻画了分部相关性的"双刃剑"效应：降低跨期配置成本和提高跨期配置空间，二者需要通过分部相关性进行取舍。模型部分通过交易成本和收益波动率两个维度进行研究，结果发现：风险越高、交易成本越低，最优分部相关性越小；收益波动率越高，交易成本对最优分部相关性的影响越弱；交易成本越低，收益波动率对最优分部相关性的影响越弱。实证部分针对中国上市公司的分部数据进行实证检验，发现中国多元化企业的最优分部相关性符合模型的推演结果。     

Robust allocation of a defensive budget considering an attacker's private information

Attackers' private information is one of the main issues in defensive resource allocation games in homeland security. The outcome of a defense resource allocation decision critically depends on the accuracy of estimations about the attacker's attributes. However, terrorists' goals may be unknown to the defender, necessitating robust decisions by the defender. This article develops a robust-optimization game-theoretical model for identifying optimal defense resource allocation strategies for a rational defender facing a strategic attacker while the attacker's valuation of targets, being the most critical attribute of the attacker, is unknown but belongs to bounded distribution-free intervals. To our best knowledge, no previous research has applied robust optimization in homeland security resource allocation when uncertainty is defined in bounded distribution-free intervals. The key features of our model include (1) modeling uncertainty in attackers' attributes, where uncertainty is characterized by bounded intervals; (2) finding the robust-optimization equilibrium for the defender using concepts dealing with budget of uncertainty and price of robustness; and (3) applying the proposed model to real data.     

An Approach for Optimal Allocation of Safety Resources: Using the Knapsack Problem to Take Aggregated Cost‐Efficient Preventive Measures

On the basis of the combination of the well‐known knapsack problem and a widely used risk management technique in organizations (that is, the risk matrix), an approach was developed to carry out a cost‐benefits analysis to efficiently take prevention investment decisions. Using the knapsack problem as a model and combining it with a well‐known technique to solve this problem, bundles of prevention measures are prioritized based on their costs and benefits within a predefined prevention budget. Those bundles showing the highest efficiencies, and within a given budget, are identified from a wide variety of possible alternatives. Hence, the approach allows for an optimal allocation of safety resources, does not require any highly specialized information, and can therefore easily be applied by any organization using the risk matrix as a risk ranking tool.     

Evaluating and improving risk formulas for allocating limited budgets to expensive risk-reduction opportunities

Simple risk formulas, such as risk = probability × impact, or risk = exposure × probability × consequence, or risk = threat × vulnerability × consequence, are built into many commercial risk management software products deployed in public and private organizations. These formulas, which we call risk indices, together with risk matrices, “heat maps,” and other displays based on them, are widely used in applications such as enterprise risk management (ERM), terrorism risk analysis, and occupational safety. But, how well do they serve to guide allocation of limited risk management resources? This article evaluates and compares different risk indices under simplifying conditions favorable to their use (statistically independent, uniformly distributed values of their components; and noninteracting risk‐reduction opportunities). Compared to an optimal (nonindex) approach, simple indices produce inferior resource allocations that for a given cost may reduce risk by as little as 60% of what the optimal decisions would provide, at least in our simple simulations. This article suggests a better risk reduction per unit cost index that achieves 98–100% of the maximum possible risk reduction on these problems for all budget levels except the smallest, which allow very few risks to be addressed. Substantial gains in risk reduction achieved for resources spent can be obtained on our test problems by using this improved index instead of simpler ones that focus only on relative sizes of risk (or of components of risk) in informing risk management priorities and allocating limited risk management resources. This work suggests the need for risk management tools to explicitly consider costs in prioritization activities, particularly in situations where budget restrictions make careful allocation of resources essential for achieving close‐to‐maximum risk‐reduction benefits.     

A zero-one goal programming approach for information system project selection

This paper presents a multi-objective model that can be used to help information systems (IS) managers decide which IS projects should be selected for development and implementation in a constrained resource environment. Developed to overcome the problems observed in currently used IS selection procedures, the model presented in this paper can be used to make decisions when IS selection goals are conflicting and measured in incommensurable units. To illustrate the use of this multi-objective approach to model IS project selection, a corporate resource allocation problem is developed and solved. Comparative results with currently used scoring and ranking methods reveals the superiority of the proposed multi-objective model.     

金融网络风险下多因子矩阵回归的资产组合与定价

本文从企业的股权、债权关系出发,基于违约距离构建无向图网络,分析了不确定性风险以网络形式进行传染、溢出和蔓延等现象,通过最小生成树的稀疏网络优化方法最大限度降低资产组合的非线性风险影响。站在资源配置的角度,利用稀疏聚类算法深入挖掘资产特征和捕捉其间的相依关系,采用多目标、多指数的稳健矩阵回归策略动态跟踪市场趋势,并通过自适应权重学习策略对网络风险叠加影响下的资产组合进行选择和配置,最终获得最小生成树风险下投资组合的稀疏聚类优化策略,进一步扩充了资产定价多因子模型。研究发现多目标矩阵回归的稀疏聚类投资组合,不仅对组合内投资标的进行了选择性舍弃,使资金能够集中配置于优质资产,更有助于通过最小生成树减缓甚至切断风险在网络中的传播,有效降低了资产之间风险的传染性。基于金融网络的风险分析方法不仅有效地刻画了风险以网络方式互相传染、互相影响、互相强化的非线性叠加效应,而且通过资产之间配置系数的压缩变换和最小生成树的优化方式,最小化最坏情形下风险传染的影响,对复杂网络环境下的资产配置和全面风险管理进行了有益补充,为长期投资基金获得风险和收益更为均衡的资产配置,提供了合意的投资策略和决策依据。     

Characterizing Environmental Harm: Developments in an Approach to Strategic Risk Assessment and Risk Management

Environmental policymakers and regulators are often in the position of having to prioritize their actions across a diverse range of environmental pressures to secure environmental protection and improvements. Information on environmental issues to inform this type of strategic analysis can be disparate; it may be too voluminous or even absent. Data on a range of issues are rarely presented in a common format that allows easy analysis and comparison. Nevertheless, judgments are required on the significance of various environmental pressures and on the inherent uncertainties to inform strategic assessments such as “state of the environment” reports. How can decisionmakers go about this type of strategic and comparative risk analysis? In an attempt to provide practical tools for the analysis of environmental risks at a strategic level, the Environment Agency of England and Wales has conducted a program of developmental research on strategic risk assessment since 1996. The tools developed under this program use the concept of “environmental harm” as a common metric, viewed from technical, social, and economic perspectives, to analyze impacts from a range of environmental pressures. Critical to an informed debate on the relative importance of these perspectives is an understanding and analysis of the various characteristics of harm (spatial and temporal extent, reversibility, latency, etc.) and of the social response to actual or potential environmental harm from a range of hazards. Recent developments in our approach, described herein, allow a presentation of the analysis in a structured fashion so as to better inform risk‐management decisions.     

Risk management in corporate planning

The risk distribution matrix (RDM) is to be applied in resource allocation and is a means of placing environmental risk in perspective. All forms of business operations should be included so that a company has a comprehensive picture of its commitments in safe, moderate, and high-risk countries. Corporate self-analysis is involved in the first three steps. The fourth step seeks to correct the risk profile through multiple strategies. Many years are likely to be required before a company achieves its desired profit/risk composition.

The advantage of the system is its individualization. Within the general framework given on the preceding pages, companies can make decisions based on factors unique to their industry, current position, preferred position and flexibility within the constraints identified. Ultimately, RDM provides a thorough evaluation system custom tailored to each company, insuring more profitable overseas transactions.